An unbelievable fact is: Although the Wright brothers drove the plane into the sky more than 100 years ago, people still don’t know how the plane flies.
From a strictly mathematical level, engineers know how to design aircraft that can fly at high altitudes, but mathematical formulas cannot explain the cause of aerodynamic lift. In order to explain this problem, the two theories are tit-for-tat, but neither can provide a complete explanation.
What generates lift in aerodynamics? The views of the various parties have not reached consensus. Scientists have proposed two different theories to explain lift. The problem is that these two non-technical theories are not wrong in themselves, but neither of them proposes a complete theory that can explain all aspects of lift.
It seems impossible to perfectly explain the lift in aerodynamics. It is necessary to consider all the forces, influencing factors and physical conditions in the process of aircraft lifting, without leaving unexplained or unknown problems. Does this theory really exist?
In the Fluid Mechanics Laboratory of NASA's Ames Center, scientists tested the flow field on the surface of the aircraft in a tank experiment. Image credit: Ian Allen
Flawed classic theory
So far, the most popular explanation for lift is the Bernoulli principle , which is a principle proposed by the Swiss mathematician Daniel Bernoulli in the monograph Hydrodynamica published in 1738. . Simply put, Bernoulli's principle states that the pressure of a fluid will decrease as the speed increases, and vice versa.
There is a special bulge above the wings of an airplane, which is called an airfoil in technical terms . Because of this curvature, the speed of the air flowing through the curved upper surface is faster than the air flowing through the flat lower surface of the wing. Scientists believe that, according to Bernoulli's principle, the increase in the velocity of the fluid on the upper surface of the wing causes the air pressure there to decrease, thereby generating upward lift.
Whether it is wind tunnel experiments (mainly observing the trajectory streamlines shown by smoke particles), nozzles or Venturi tubes (a kind of vacuum generating device) and other experiments, they have given a huge amount of empirical data. These data strongly prove the correctness of Bernoulli's principle. However, Bernoulli's principle alone cannot fully explain lift. Although actual experience shows that the air flow is indeed faster on a curved surface, the Bernoulli principle cannot explain why the flow rate becomes faster. In other words, this theorem does not explain how the high velocity above the wing is generated.
A well-known demonstration, which has repeatedly appeared on many network platforms and even some textbooks, claims to be able to "show" Bernoulli's principle. In this demonstration, the experimenter will place a piece of paper horizontally in front of the mouth and blow its upper surface with air. At this time, the paper surface will rise. People use this to show that the Bernoulli effect does exist. However, when you blow the bottom surface of the paper, the surface of the paper will still rise. It stands to reason that the paper should have the opposite result, because the airflow at the bottom of the paper should pull the paper down.
Holger Babinsky is a professor of aerodynamics at the University of Cambridge in the United Kingdom. He pointed out that the airflow on one side will raise the curved surface of the paper. "This is not because the air velocity on both sides of the paper is different. ". To illustrate this point, you can blow a straight sheet of paper to verify all this. For example, blow a piece of vertically suspended paper to see if it moves neither to one side nor to the other. After all, "despite the obvious difference in air velocity, the pressure on both sides of the paper is the same."
The second disadvantage of Bernoulli's principle is that it does not explain why the high-speed air flowing over the upper wing forms a lower pressure, rather than a higher pressure. After all, when the wing moves upward, the air should be compressed, and the pressure on the top of the wing should increase. In daily life, this "bottleneck phenomenon" usually slows things down rather than speeding them up. For example, on an expressway, when two or more lanes are merged into one, the vehicles on the road will not drive faster, but will decelerate in traffic flow, and even traffic jams may occur. The air molecules flowing on the upper surface of the wing are not like this, but Bernoulli's principle does not explain why this phenomenon occurs.
The third question is particularly critical. It can prove that Bernoulli’s interpretation of lift is wrong: an airplane with a curved upper surface can fly even when turned over. In this case, the curved wing surface becomes the bottom surface. According to Bernoulli's principle, the pressure on the lower surface of the wing will be reduced. When this low-pressure environment is combined with the action of gravity, it should have the effect of pulling the aircraft downward, rather than supporting it to continue flying. However, whether it is an airplane with a symmetrical airfoil (the curvature of the top and bottom are equal), or an airplane with a flat airfoil on the upper and lower surfaces, as long as the wing meets the oncoming wind and cooperates with the appropriate wind The horns can be turned over and fly. This means that Bernoulli's principle alone is not sufficient to explain the cause of lift.
Using Bernoulli's Principle to Explain the Defects of Wing Lift
In addition to using Bernoulli's theory to explain lift, scientists also tried to use another theory to explain the source of this force: Newton's principle of force and reaction . According to this law, when the wing pushes the air downward, the mass of air will produce an upward thrust of equal magnitude and opposite direction, that is, lift. Therefore, the theory is that the wing generates lift by pushing the air. This theory applies to wings of any shape, curved or flat, symmetrical or asymmetrical. At the same time, this theory also applies to airplanes that are flying normally, or flying upside down. Therefore, Newton's third law has a more comprehensive explanation of lift than Bernoulli's principle, and it can deal with more situations.
But as far as the theory itself is concerned, the acting force and reaction force cannot explain the low pressure area on the top of the wing , and the existence of this area has nothing to do with whether the wing is bent. Only when the plane lands and stops flying, the low pressure area above the wing will disappear, making the top and bottom the same, returning to the surrounding air pressure. However, as long as the aircraft is flying, the low-pressure zone is a factor that cannot be ignored in aerodynamics. It must be explained to explain why the aircraft can fly.
Therefore, whether it is Bernoulli's principle or Newton's third law, they are correct from their respective perspectives, and they are not contradictory to each other. However, the problem is that no one theory can fully explain lift, and the combination of the two cannot work, because both of them miss something.
Theory development history
You know, neither Bernoulli nor Newton thought of using their own theories to explain the lift of airplanes. Their respective lives are still a long time away from the age of flight. When the Wright brothers succeeded in flying the plane into the sky, contemporary scientists urgently needed to understand the lift in aerodynamics and explain the secrets behind the flight. These two theories were rediscovered and applied.
In the early 20th century, several British scientists advanced the technology of lift and related mathematical theories. They believe that air is a perfect fluid, which means it is incompressible and has zero viscosity. Although this is different from the actual characteristics of air, it is understandable for scientists who need to understand and control the flight of mechanical equipment, because it will make mathematical calculations simpler and more direct. But this simplification also requires a corresponding price: in an ideal incompressible gas, no matter how successful the calculated airfoil is mathematically, it will show various defects in practical applications.
Albert Einstein (Albert Einstein) also devoted himself to the study of lift issues. In 1916, Einstein gave an explanation based on the incompressible and frictionless fluid (that is, the ideal fluid hypothesis). Although Bernoulli’s name was not mentioned, he gave an explanation basically consistent with Bernoulli’s principle. He said that the fluid pressure is greater where the speed is slower, and vice versa. In order to take advantage of these pressure differences, Einstein proposed a slightly raised design on the top of the wing. This shape can increase the airflow velocity at the raised area, thereby reducing the pressure there.
Einstein might think that analysis based on ideal fluids is also applicable to fluids in the real world. In 1917, on the basis of theory, Einstein designed a type of wing called cat's-back wing (because its shape is similar to a cat that is stretching). Subsequently, he brought the design proposal to Berlin-based aircraft manufacturer LVG. The company built a new aircraft around the design plan. But the test pilot reported that the plane was wobbly in the air, like "a pregnant duck." In 1954, Einstein stated that his brief involvement in the aviation industry was more like a "stupid behavior of young people."
Complete lift theory?
Nowadays, the scientific method of designing airplanes is to use computational fluid dynamics (CFD) simulations and to calculate Navier-Stokes equations that fully consider the actual viscosity of real air. The results obtained by CFD simulation and the solution of the above equation can predict the pressure distribution pattern, and give the air flow pattern and quantitative results. Today's aircraft design field has been very advanced, and it can be said that these technologies are the foundation of the industry. However, they themselves do not make a physical and qualitative explanation of lift.
In recent years, the well-known American aerodynamicist Doug McLean has tried to transcend pure mathematics and set out to deal with the physical relationship during flight. This relationship may explain the various characteristics of lift in reality. . In 2012, he proposed a new interpretation of wing lift in his book.
When explaining lift, McLean also started from the most basic assumption in aerodynamics: the air around the wing is "a continuous medium that deforms according to the shape of the wing." This deformation will exist in the form of fluids appearing above and below the wing. McLean wrote: "In a large area called the pressure field, the wing will affect the air pressure." When lift is generated, a low-pressure diffusion air mass is always formed above the wing, and high pressure is usually formed under the wing. The diffusion air mass. When these air masses act on the wing, they form a pressure difference that generates lift on the wing.
Throughout the process, the wings push the air downward, causing the airflow to deflect downward. The air above the wings is accelerated according to Bernoulli's principle. There is a high pressure area under the wing and a low pressure area above the wing. This means that in McLean’s interpretation of lift, there are four necessary components: the airflow turns downward, the airflow speed increases, the low-pressure zone and the high-pressure zone .
It can be said that the interrelationship between these four elements is the most novel and unique place in McLean's narrative. He wrote: "They support each other in a causal relationship, and any one of them can't appear without the other three." The pressure difference exerts lift on the airfoil, while the downward turning of the airflow and the change of the flow rate maintain it. Differential pressure. It is in this system of mutual influence that the fifth element explained by McLean appears: the interaction between the four elements . It seems that these four elements must appear at the same time, influence and induce each other, in order to maintain each other.
There seems to be a kind of magic in this synergy. In McLean's description, it is like four active individuals, only to help each other to maintain together in the air. In other words, as he admitted, this is a case of "circular causality". However, "how does each of the interacting factors maintain and strengthen the other factors?" What causes this dynamic system of interaction, reciprocity, and mutual influence? McLean's answer is: Newton's second law of motion .
Newton's second law states that the acceleration of an object or fluid is proportional to the force exerted on the object. McLean said: "Newton's second law tells us that when the pressure difference exerts a resultant force on the fluid mass, it will inevitably cause the velocity or direction (or both) of the fluid mass to change." But conversely, there is a pressure difference. Whether or not and the size change is also determined by the acceleration of the fluid mass.
Have we gained some energy out of thin air in this process? McLean believes that there is no such thing. If the wings are at a standstill, none of the factors in this mutually reinforcing system will exist. Only when the wing is moving in the air, each fluid mass will affect all other fluid masses. The entire flight process supports the existence of this set of mutually stimulating and interdependent factors.
Improved lift theory
Soon after proposing this explanation, McLean realized that he had not fully considered all factors related to lift in aerodynamics, because it was unconvincing to explain why the pressure above the wing was different from the surrounding environment. Therefore, McLean published an article in The Physics Teacher in the November 2018 issue of The Physics Teacher, providing a "comprehensive explanation" of the lift in aerodynamics.
Although this article reiterated McLean’s previous arguments to a large extent, he also made further attempts to better explain what causes the unevenness of the pressure field and why it presents this unique physical form. . In addition, he also introduces new argument flow field (flow field) level interaction, that such non-uniform pressure field is caused by one kind of force, a downward force is exerted on the wings of the air .
Whether in his book or in a follow-up article, whether McLean fully and correctly explained the mechanism of lift remains to be further explained and discussed. We can also see that due to various reasons, it is difficult to give a clear, simple and satisfactory explanation of aerodynamic lift.
Nevertheless, there are only a few outstanding issues that we need to explain further. Regarding lift, you should be able to recall that this is the result of the pressure difference between the upper and lower surfaces of the wing. We already have an acceptable explanation for the lower surface of the airfoil : oncoming air squeezes the wing, generating lift in the vertical direction and drag in the horizontal direction. The force that squeezes the lower surface of the wing upward appears in the form of local high air pressure. Simply put, this higher air pressure is the result of acting and reaction forces.
However, the situation on the upper surface of the wing is quite different. There is a low pressure area, which is an important part of providing lift. However, if neither Bernoulli's principle nor Newton's third law can explain it, what can explain it? From the streamline information in the simulation experiment, we can know that the air above the wing is closely connected with the downward curve of the airfoil. But why does the air mass flowing over the upper surface of the wing have to flow along the wing that is bent downward after the bulge? Why can't you leave it and fly directly back?
Mark Drela, a professor of fluid dynamics at the Massachusetts Institute of Technology, gave an answer: "If these fluid masses deviate from the upper surface of the wing momentarily, the space between it and the wing will form "Vacuum," he explained, "this vacuum will suck down the fluid mass until the vacuum is almost filled. That is, until the direction of their flow is tangent to the wing again. This is forcing the fluid mass to move along the shape of the wing. The physical mechanism of the airfoil. The presence of a slight vacuum environment locally can cause the fluid mass to flow along the curved surface of the wing."
The deviation of the air mass, and the process of being drawn in, caused a low pressure in the upper surface area of the wing. This process also triggers another effect: the air flows faster on the upper surface of the wing. "When the airflow above the wing approaches the wing, the low-pressure air mass on the upper surface of the wing will'pull' the airflow in the horizontal direction. Therefore, when the air reaches the wing, it will travel faster," Drela said. "So, the increase in air velocity above the wing can be seen as a secondary effect of pressure reduction."
But as always, different experts will give different answers when explaining lift. Babinsky, an aerodynamicist at the University of Cambridge, said: "I respect my colleague Dreira, so I am very reluctant to oppose his views. However, if the appearance of a vacuum is the cause of the lift, it is very It’s difficult to explain why sometimes the airflow does not flow across the surface of the wing. Of course, he is correct in other respects. There may be no simple and quick explanation for this question."
Dreira himself admitted that his explanation was not satisfactory in some respects. He said: "An obvious problem is that no explanation will be universally accepted." It seems that to this day, there is still no simple answer to this question.
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